Today, Tony the Alpaca needs some help with an array he found in the grass!

Tony gives you an array $a$ of length $N$. He has $Q$ queries to ask you about the array. Each query is of the form $l_i$, $r_i$, $x_i$, such that $l_i\le r_i$.

Given these parameters, Tony wants to know if there are $2$ distinct indices $p$ and $q$ between $l_i$ and $r_i$ inclusive such that $a_p\cdot a_q=x_i$.

Also, since Tony hates numbers that are the same, $a_p$ must not be equal to $a_q$. To keep Tony happy, you must answer all his queries!

Constraints

$1\le N\le {10}^6$

$1\le Q\le 5\cdot {10}^4$

$1\le a_i\le {10}^5$

$1\le l_i\le r_i\le N$

$1\le x_i\le {10}^5$

Subtask 1 [10%]

$1\le N,Q,a_i\le {10}^3$

Subtask 2 [90%]

No additional constraints.

Input Specification

The first line of input contains two integers $N$ and $Q$.

The second line of input contains $N$ integers $a_i$.

The final $Q$ lines will each contain $l_i,r_i,x_i$, the parameters for the $i^{th}$ query.

Output Specification

For each query, output YES if there are two distinct indices that multiply to $x_i$, and NO otherwise.

Sample Input 1

5 3
1 5 5 2 3
1 3 25
1 4 6
1 5 10

Sample Output 1

NO
NO
YES

Sample Input 2

6 4
2 4 2 4 2 4
1 3 8
1 6 5
1 2 1
1 5 16

Sample Output 2

YES
NO
NO
NO